Cummins Capital Flashcards
RAROC Formula
RAROCi = Net Incomei / Allocated Capitali
EVA and EVAOC Formula
EVAi = Net Incomei - ri x Allocated Capitali
EVAOCi = Net Incomei / Allocated Capitali - ri
where ri is the CAPM required Rate of Return
Pure Play Approach
Find firms that offer only one line of business and use them to estimate the cost of capital for a line.
The problem with this is that it’s difficult to find firms that write only one line and the underwriting characteristics may be significantly different.
Use “full-information betas” to estimate the cost of capital by using regressions on multi-line firms.
Beta Equity Formula
Beta Equity = Beta Assets x (1 + Summation L&LAE Reservesi / Surplus) + Summation Betai x (Premiumi / Surplus)
Beta Equity and Cost of Equity Capital Formula
Beta Equity = Beta Assets x (1 + Summation L&LAE Reservesi / Surplus) + Summation Betai x (Premiumi / Surplus)
re = rf + Be (rm - rf)
Required rate of underwriting return for each line
rd = - Loss&LAE Reservesi / Surplus x rf + Betai x (rm - rf)
Problems with using the CAPM Model to allocate capital
CAPM reflects systemic underwriting risk, the correlation of underwriting with the market portfolio. However, insurers are also concerned about the risk of extreme events. The required return should reflect this risk as well.
Underwriting betas by line of business are difficult to estimate.
Rates of return are also driven by other factors besides beta, but the CAPM model ignores these other factors.
VaR Exceedence Probability to calculate capital
(E[Lossi] + Capitali) / E[Lossi] = Factor from graph or chart
Exceedance probability is the probability that the loss for a line of a business will be greater than the expected loss plus the allocated capital for the line.
Goal is to set the capital for each line such the the exceedance probability is the same for all lines and set at the target.
Problems using VaR
A firm might not have enough capital so that all business meet a particular exceedance probability level. In this case, the firm could raise the probability level or raise more capital.
Stand-alone exceedance probability doesn’t reflect the diversification benefit.
Unlike EPD, VaR doesn’t reflect the amount by which losses might exceed the exceedance probability level.
EPD graph to calculate capital
(Liabilitiesi + Capitali) / Liabilitiesi = Assets to Liabilities factor from graph or chart
Goal is to set the capital so that each business unit has the same EPD ratio.
EPD for Captial Advantages/Disadvantages:
Advantages
- Better than VaR because it reflects the expected amount that may be lost at a probability level.
- VaR only looks at the specific loss value that would be exceeded at the probability
Disadvantages
- Doesn’t take into account the impact of diversification across LOBs.
Merton-Perold (MP) Method Procedures
Obtain joint risk capital required for the insurer that excludes the individual lines.
Subtract the joint risk from the total risk to calculate each stand-alone.
Extra capital is allocated to corporate.
Merton-Perold (MP) Additional Information
Goal is to reflect the benefit of diversification. Can be seen here as a portion is unallocated to the line.
This method results in higher EVA and RAROC than using the stand-alone capital allocation or if the total capital was allocated with no allocation to corporate.
Full allocation will result in a firm rejecting some profitable projects.
Good for when adding an entire business to the insurer.
Meyers-Read (MR) Additional Information
Capital is allocated by looking at the marginal impact of very small changes to the loss liabilities of an LOB on the overall capital need for the insurer.
Allocates 100% of capital. So better for normal operations.
Advantages
- More intuitive?
- Adds to 100% capital
- Decision making usually involves small changes to an existing portfolio
Impact of covariances on the allocation
When the covariance between the loss of line i and the insurer’s total loss is higher the surplus allocation is higher (when higher losses then the line is relatively riskier).
When the covariance between the loss of line i and the insurer’s asset portfolio is higher the surplus allocation is lower (when higher losses it’s likely assets will be higher creating a hedge).
